from lib_prime import primes


def r_modulo_closed_form(n, m):
    assert n > 0 and m > 0
    return ((pow(10, n, 9 * m) - 1) // 9) % m


def is_factor(n, m):
    return pow(10, n, 9 * m) == 1


def repunit_factor_sum(n):
    ps = []
    for p in primes(10**6):
        assert is_factor(n, p) == (r_modulo_closed_form(n, p) == 0)
        if r_modulo_closed_form(n, p) == 0:
            ps.append(p)
        if len(ps) == 40:
            break
    return sum(ps)


def euler_132():
    assert repunit_factor_sum(10) == 9414
    return repunit_factor_sum(10**9)

if __name__ == "__main__":
    solution = euler_132()
    print("e132.py: " + str(solution))
    assert solution == 843296